Web surfers at a site called the Democratic Underground think Virginia Gov. Mark R. Warner should be their party's next presidential candidate. So does a guy named Steve, who has started a "Warner in 2008" Internet journal. And among political pundits and the soul-searching leadership of the Democratic Party, Warner's name keeps popping up.

Three years ago, Warner persuaded voters in an overwhelmingly red state to put him in office with a NASCAR-loving, pro-death penalty, pro-gun rights, fiscally conservative campaign. Since then, he has backed some restrictions on abortion, signed more than a dozen gun rights bills, balanced the state's books and persuaded a Republican legislature to help him pass a $1.5 billion tax increase.

Now, as Democrats lick their wounds 1,452 days before the next presidential election, some are wondering whether Warner could work the same magic across the South, providing the party a presidential candidate who could appeal to the conservative, heartland voters who helped reelect President Bush.

"He clearly did something that Democrats have had trouble doing, that is, relating to rural voters," said Joe Trippi, who managed Howard Dean's primary campaign for president. "Howard Dean, Hillary Clinton -- the standard names -- would do a lot worse than study Mark Warner."

The notion of a presidential bid by Warner could ripple through Virginia politics. The state's voters have not been kind to governors who seem too eager to move on, and Warner's full-time support will be key to Democratic Lt. Gov. Timothy M. Kaine's chances of succeeding Warner next year. A Warner presidential campaign would also change the political calculations about whether he might challenge U.S. Sen. George Allen (R), who is up for reelection in 2006.

Trippi and others say it is way too early to think seriously about a 2008 nominee. But in the past week, Warner's name has been all over television news shows and in newspapers.

He was mentioned, along with a few other possibilities, in the Los Angeles Times, the New York Times, the Sunday Times of London, the Weekly Standard and the Wall Street Journal. They talked about him on CNN's "Inside Politics." And disaffected Democrat Zell Miller, the senator from Georgia, listed him among a group of "very, very good candidates" in an appearance on Fox News.

Warner, who is entering his fourth and last year as governor, declines to talk about his political future, other than to specifically deny any interest in becoming chairman of the Democratic National Committee. He professes only a laserlike focus on his state and his role as chairman of the National Governors Association.

"I'm just not going to comment on any of that," he said as he boarded a plane for a national governors forum on education in Cleveland. "My top, sole responsibility is to be governor of Virginia. Other than the hardest of the hard core, most Americans are pretty well exhausted by this election."

But Warner, who graced the cover of Governing magazine this month as a public official of the year, has not been shy about describing how he thinks the Democratic Party must change. And those assessments fuel speculation about his role in the party's future.

"The Democratic Party can't write off two-thirds of the country," he said. "There were a number of voters in parts of rural Virginia and across the country who never got to a real review of John Kerry's plans on health care or education or job growth because [he's] . . . a Massachusetts senator. They never got past the label."

Some Democrats warn that a centrist candidate like Warner could be seen as "Republican light," standing for little.

"The number one candidate for the liberal wing would probably be Senator Clinton," said John Pitney, a politics professor at Claremont McKenna College. "The question is, do the Democrats go with their head or their heart?"

Pitney said the logical choice might be someone such as Warner, who is fiscally conservative and has won in a conservative state.

"The Democratic Party needs to do now what we did during the period between 1989 and 1992," said Al From, the founder of the Democratic Leadership Council. "It needs to redefine itself by challenging a lot of the old orthodoxies. Mark Warner's biggest contribution to our party can be redefining our brand and what it stands for."

One challenge for Warner is finding something to do after he leaves office. Virginia's constitution prohibits governors from succeeding themselves.

From said he has begun talking with Warner about playing a leading role at the Democratic Leadership Council. Others have speculated that Warner still might challenge Allen. Or the governor, a millionaire, could simply travel the country campaigning for candidates and gathering support.

The director of Warner's political action committee said the recent attention has prompted calls from across the country as she plans a major fundraiser at the Tysons Corner Ritz-Carlton for his 50th birthday next month. Steve Jarding, Warner's former campaign manager, said name recognition will not be a problem.

"When Bill Clinton was governor, the only thing we knew as Democrats was that he gave a long, boring speech at the Democratic convention," Jarding said.

And there's evidence that people already know Warner's name.

At one site, www.democraticunderground.com, Warner was listed as a possible candidate along with former vice president Al Gore, Hillary Clinton and three others. Out of 127 votes cast, Warner got the most: 53. Not all of the site's visitors were convinced, however. One person wrote, "He seems really boring."

Another Web site, warner2008.blogspot.com, went up days after the election. The site's author, who identifies himself only as "Steve," writes enthusiastically about Warner, saying that he "sponsored a NASCAR vehicle, used a bluegrass song as his campaign theme, and managed to retain core Democratic values without alienating rural voters."

That's just the kind of candidate Republicans worry about, said Arkansas Gov. Mike Huckabee (R), one of Warner's closest political friends. Huckabee said Democrats have a tough time in southern and rural states.

"They don't understand us," Huckabee said. "We live real lives. We shop and use coupons to buy things, and we manage our budgets carefully. We know what the price of gas is, and it matters when it goes up. We have to think about vacations and if possible find the discount airfares."

Huckabee said Warner could connect with those people.

"I'm glad they didn't turn to him this time," he said. "Frankly, it might mean all my friends in Washington would be looking for jobs."

"The Democratic Party can't write off two-thirds of the country," Virginia Gov. Mark R. Warner says.